(1): Consider the set of the smallest 6 odd primes: {3,5,7,11,13,17}.
What is the largest multiple of this product which has distinct digits ?

(2) What is the maximum number of digits a square-free integer (whether even or odd) can have if its digits are all distinct?

(3) What is the largest odd square-free integer with distinct digits having exactly n prime factors for n = 1,2,3,4,5? You can extend this to larger numbers of factors if you wish.

Note: a square-free integer is one whose prime factorization has exactly one factor for each prime that appears in it.

Note that in Part 1, only the first 6 odd primes are included:  {3,5,7,11,13,17}.

Posted by Larry on 2021-07-25 09:44:57